The purpose of this note is to draw attention to an interesting problem in the history of mathematics which the pressure of work will prevent me from taking up, and to make a suggestion about a possibly neglected aspect of the problem that should be explored. The problem is: to describe the origins of the concept of a vector space and its recognition as a central topic in mathematics. Moves towards the explicit treatment of topics, and their axiomatization, are always of interest; in addition, it seems that vector spaces have had a curious and convoluted development.